A note on “Convergence and best proximity points for Berinde's cyclic contraction with proximally complete property”

Abstract

Recently, Sanhan and Mongkolkeha introduced the concept of Berinde's cyclic contraction, and they established some results. Unfortunately, these results seem to be incorrect. In this paper, some counterexamples are given.

Best Proximity Points for Alternative Maps

“…One can easily see that a cyclic map is a special case of an alternative map. Due to Fan [4], many authors publish their papers with their Best Proximity Points in [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]:…”

Best Proximity Point Theorems for a Berinde MT-Cyclic Contraction on a Semisharp Proximal Pair

“…Several years later, the above result has been studied and generalized by many researchers, such as Reich [4], Sehgal and Singh [5], Vetrivel et al [6], Anuradha and Veeramani [7], Basha [8,9], Kirk et al [10], Raj [11], Gabeleh [12], Abkar 2 International Journal of Mathematics and Mathematical Sciences and Gabeleh [13], Eldred and Veeramani [14], and Du and Lakzian [15] and references therein. Some recent research papers worth mentioning are [16][17][18][19].…”